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Signatures of the vulcanization transition--amorphous solidification inducedby the random crosslinking of macromolecules--include the random localizationof a fraction of the particles and the emergence of a nonzero static shearmodulus. A semi-microscopic statistical-mechanical theory is presented of thelatter signature that accounts for both thermal fluctuations and quencheddisorder. It is found (i) that the shear modulus grows continuously from zeroat the transition, and does so with the classical exponent, i.e., with thethird power of the excess cross-link density and, quite surprisingly, (ii) thatnear the transition the external stresses do not spoil the spherical symmetryof the localization clouds of the particles.Comment: REVTEX, 5 pages. Minor change

Elasticity near the vulcanization transition